Do you have access to office supplies and way too much time on your hands? Then, this is your opportunity to build a Super Pencil Ball!

The Materials

You will need 60 unsharpened pencils, a roll of masking tape and a pair of scissors.

You will also briefly require a ruler and a sheet of paper. Cut a tiny strip of paper approximately 9.5 millimeters wide. This strip will aid in spacing out the pencils during the first phase of construction.

Triangle Phase

In this phase, you will construct equilateral triangles by taping 3 pencils together.

Note that the pencils are arranged eraser-end to unsharpened-end. Also, there is V-shaped gap where the pencils meet.

As you will see below, the strip of paper will aid in maintaining this gap.

Cut a square of masking tape and place it sticky-side up on a flat surface. Stick one of the pencils to the tape as shown below.

Note that the pencil is positioned toward the top end of the tape. And, since tape adheres better to wood than to metal or rubber, a tiny portion of the yellow surface of the pencil is situated over the tape.

Lightly place the paper strip directly to the right of the eraser.

Place a second pencil onto the tape directly to the right of the paper strip.

Carefully peel the paper strip off of the tape. You will repeatedly use it to space pencils apart.

Roll the tape around the pencils while maintaining the space between them.

The pencils will now be joined together concealing a hidden gap as shown below.

Repeat this process to form a chain of 3 pencils.

Bend the chain to form a triangular shape.

The hidden gaps will become the aforementioned V-shaped gaps. You may need to adjust the width of the paper strip depending on radius of the pencil you are using.

Apply a strip of masking tape over the exposed terminals being sure to create the third V-shaped gap.

Masking tape is surprisingly pliable. Bend it around the pencil ends.

To further secure the connection, apply a second piece of tape underneath the pencils as shown below.

Your first triangle is now complete.

Produce a stack of 20 triangles.

Pyramid Phase

Place 2 triangles together on a flat surface.

Be sure to arrange the triangles such that the pencils in contact are pointed in opposite directions. In the image below, the unsharpened-tip end coincides with the arrow tip. The metal band on the eraser end is the widest part of the pencil. Consequentially, this arrangement will even things out.

While tightly squeezing the pencil pair together, apply a thin strip of tape to one end. Make sure that the strip of tape only covers the top surface of the pencils. Do not wrap tape all the way around. As you will see below, this strip of tape situated as such will act like a hinge.

Apply a second strip of the tape to the opposite end. Pad it down as shown below.

Repeat this process to attach 5 triangles together in a circular pattern.

Carefully flip it over. In the image below, note that tape strips were only on one side as mentioned.

Cut another strip of tape and have it ready for the next step.

Lift the center upward to form a pyramid with a pentagonal base. Apply the tape strip to the outside to hold the structure together.

Note that the tape strips on the internal sides are acting as the aforementioned hinges.

Make sure that the pencils are properly aligned and then add a second piece of tape at the opposite end.

Firmly squeeze the pencils together as you wrap a longer strip of tape all the way around them, covering the thin strip added earlier.

Repeat the wrapping step for all 10 pencil-pair ends.

This completes one pyramid.

Use 5 more triangles to construct a second pyramid. However, pay attention to the arrangement of pencils around the pyramid's base. As shown in the image below, the pencils of the first pyramid were arranged counterclockwise. In the second pyramid, arrange them clockwise. This orientation is not critical, but it will balance everything out more precisely.

Ring Phase

On a flat surface, lay the remaining 10 triangles out in a truss design. As in the prior phase, apply thin strips of tape to the top sides to hold the triangles together. Again, do not wrap the tape all the way around as the strips will act as hinges.

Cut 2 more thin strips of tape in preparation for the next step.

Lift up the truss design and wrap it into a ring. Apply the 2 tape strips to the outside to hold the ring together. In the image below, note that the "hinges" are in the interior of the ring.

At this point, held together only by the interior "hinges", the ring is fairly unstable. Adjust it until the lower and upper surfaces form regular pentagons.

As in the prior phase, tightly wrap the pencil-pair ends with longer strips of tape covering the "hinges". As you do this, adjust the pencils to maintain the aforementioned regular pentagons.

This completes the ring.

Assembly Phase

Lower one of the pyramids onto the ring. As mentioned, to balance things out, select the pyramid with the base that complements the top of the ring. That is, if the pencils at the top of the ring are arranged clockwise, use the pyramid with the counterclockwise base, and vice versa.

At this point, the ring and the pyramid are still somewhat flexible. Use thin strips of tape on the outside surfaces to assist in alignment. When everything is aligned, wrap longer strips of tape around the pencil-pairs as before.

Flip the structure over.

Attaching the second pyramid is the most difficult part of the assembly because the opening will not be level with the structure resting on one of the triangles of the first pyramid. To make the job easier, cut at least 5 thin strips of tape before the next step.

Lower the second pyramid over the regular pentagonal opening of the structure. Use the thin strips of tape to align the pencil-pairs. When everything is aligned, wrap longer strips of tape around the ends as before.

This completes the Super Pencil Ball!

To give you a better sense of scale, in the image below, a 1.5 liter water bottle was lowered into the Super Pencil Ball. It is resting on a sheet of printer paper.

WTF?

The Super Pencil Ball is an icosahedron, a regular polyhedron with 20 identical equilateral triangular faces, 30 edges and 12 vertices. As such, it could have been constructed with only 30 pencils. But, this design, based on chaining together equilateral triangles, makes working out the angles effortless. Also, the result is a very sturdy structure as each equilateral triangle was strengthened individually.

You can hang your Super Pencil Ball and consider it a model of a virus as many viruses, such as Herpes Simplex or HIV, have icosahedral-shaped shells. Alternatively, you can cover each face of your Super Pencil Ball with a numbered triangular-shaped piece of paper and use it as a twenty-sided die for traditional role-playing games like Dungeons & Dragons. Or, instead of numbers, you can use various answers to yes-no questions, effectively turning it into a Magic 8-Ball die.

As for me, I will continue to enlarge the Super Pencil Ball to the point that I can live in a geodesic sphere made of pencils and masking tape because I have nothing better to do.